Dynamic Riemannian Geometry of the Ising Model

A general understanding of optimal control in non-equilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the non-equilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the 2D Ising model in order to study optimal protocols for reversing the net magnetization.Comment: 5 pages, 3 figure

Rough interfaces, accurate predictions: The necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing in particular the importance of interfaces that emerge in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here we show that a coarse-grained lattice model in the spirit of those pioneered by Chandler and coworkers, when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many standard deviations from the mean, and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, as the model is fully specified by well-known properties of liquid water. As illustrative examples of its utility, we characterize the free energy profile for a solute crossing the air-water interface, and compute the thermodynamic cost of evacuating the space between extended nanoscale surfaces. Together, these calculations suggest that a highly reduced model for aqueous solvation can serve as the basis for efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.Comment: 14 pages, 7 figure

A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems

Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamical fluctuations of the controlled system. We provide a new, physically transparent derivation of a metric tensor for which the length of a protocol is proportional to its dissipation. This perspective simplifies nonequilibrium optimization problems by recasting them in a geometric language. We then describe a numerical method, an instance of geometric minimum action methods, that enables computation of geodesics even when the number of control parameters is large. We apply these methods to two models of nanomagnetic bits: a simple Landau-Lifshitz-Gilbert description of a single magnetic spin controlled by two orthogonal magnetic fields and a two dimensional Ising model in which the field is spatially controlled. These calculations reveal nontrivial protocols for bit erasure and reversal, providing important, experimentally testable predictions for ultra-low power computing.Comment: 9 pages, 2 figure

Near-optimal protocols in complex nonequilibrium transformations

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols which minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased towards a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.Comment: 6 pages and 3 figures plus 4 pages and 5 figures of supplemental materia

Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines

In a stochastic heat engine driven by a cyclic non-equilibrium protocol, fluctuations in work and heat give rise to a fluctuating efficiency. Using computer simulations and tools from large deviation theory, we have examined these fluctuations in detail for a model two-state engine. We find in general that the form of efficiency probability distributions is similar to those described by Verley et al. [2014 Nat Comm, 5 4721], in particular featuring a local minimum in the long-time limit. In contrast to the time-symmetric engine protocols studied previously, however, this minimum need not occur at the value characteristic of a reversible Carnot engine. Furthermore, while the local minimum may reside at the global minimum of a large deviation rate function, it does not generally correspond to the least likely efficiency measured over finite time. We introduce a general approximation for the finite-time efficiency distribution, $P(\eta)$, based on large deviation statistics of work and heat, that remains very accurate even when $P(\eta)$ deviates significantly from its large deviation form.Comment: 10 pages, 3 figure

Universal energy-speed-accuracy trade-offs in driven nonequilibrium systems

Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The connection between measure theoretic optimal transport and dissipative nonequilibrium dynamics provides a language for quantifying this cost and has resulted in a collection of "thermodynamic speed limits", which argue that the minimum dissipation of a transformation between two probability distributions is directly proportional to the rate of driving. Thermodynamic speed limits rely on the assumption that the target probability distribution is perfectly realized, which is almost never the case in experiments or numerical simulations. Here, we address the ubiquitous situation in which the external controller is imperfect. As a consequence, we obtain a lower bound for the dissipated work in generic nonequilibrium control problems that 1) is asymptotically tight and 2) matches the thermodynamic speed limit in the case of optimal driving. We illustrate these bounds on analytically solvable examples and also develop a strategy for optimizing minimally dissipative protocols based on optimal transport flow matching, a generative machine learning technique. This latter approach ensures the scalability of both the theoretical and computational framework we put forth. Crucially, we demonstrate that we can compute the terms in our bound numerically using efficient algorithms from the computational optimal transport literature and that the protocols that we learn saturate the bound

Data-efficient generation of protein conformational ensembles with backbone-to-side chain transformers

Excitement at the prospect of using data-driven generative models to sample configurational ensembles of biomolecular systems stems from the extraordinary success of these models on a diverse set of high-dimensional sampling tasks. Unlike image generation or even the closely related problem of protein structure prediction, there are not currently data sources with sufficient breadth to parameterize generative models for conformational ensembles. To enable discovery, a fundamentally different approach to building generative models is required: models should be able to propose rare, albeit physical, conformations that may not arise in even the largest data sets. Here we introduce a modular strategy to generate conformations based on ``backmapping'' from a fixed protein backbone that 1) maintains conformational diversity of the side chains and 2) couples the side chain fluctuations using global information about the protein conformation. Our model combines simple statistical models of side chain conformations based on rotamer libraries with the now ubiquitous transformer architecture to sample with atomistic accuracy. Together, these ingredients provide a strategy for rapid data acquistion and hence a crucial ingredient for scalable physical simulation with generative neural networks

Microscopic origin of tunable assembly forces in chiral active environments

The fluctuations of a nonequilibrium bath enable dynamics inaccessible to any equilibrium system. Exploiting the driven dynamics of active matter in order to do useful work has become a topic of significant experimental and theoretical interest. Due to the unique modalities controlling self-assembly, the interplay between passive solutes and the particles in an active bath has been studied as a potential driving force to guide assembly of otherwise non-interacting objects. Here, we investigate and characterize the microscopic origins of the attractive and repulsive interactions between passive solutes in an active bath. We show that, while assembly does not occur dynamically for achiral active baths, chiral active particles can produce stable and robust assembly forces. We both explain the observed oscillatory force profile for active Brownian particles and demonstrate that chiral active motion leads to fluxes consistent with an odd diffusion tensor that, when appropriately tuned, produces long-ranged assembly forces